i) The light intensity at a depth of 300 feet is approximately 0.131 lumens.
ii)The light intensity of 5 lumens is reached at a depth of approximately 106.6 feet.
iii)The light intensity at the surface of the water is 12 lumens.
The equation given is:
[tex]d= -425log(\frac{I}{12} )[/tex]
where d is the depth in feet, and l is the light intensity in lumens.
i)To find the intensity of light at a depth of 300 feet:
[tex]d= -425log(\frac{I}{12} )[/tex]
[tex]or, \frac{d}{-425}=log(\frac{I}{12})[/tex]
[tex]or, 10^{\frac{d}{-425}}=\frac{I}{12}[/tex]
[tex]or, 12 X 10^{\frac{d}{-425}}=I[/tex]
Given, d= 300 feet. Hence,
[tex]or, 12 X 10^{\frac{300}{-425}}=I[/tex]
or, I = 0.131 lumens (approx.)
ii) We have been given the equation :
[tex]d= -425log(\frac{I}{12} )[/tex]
when I =5 lumens
[tex]d= -425log(\frac{5}{12} )[/tex]
or, d = 106.6 feet (approx.)
iii) For finding the light intensity at the surface of the water d=0
[tex]d= -425log(\frac{I}{12} )[/tex]
Putting d = 0 we get
[tex]0= -425log(\frac{I}{12} )[/tex]
[tex]or, log(\frac{I}{12})=0[/tex]
[tex]or, \frac{I}{12} = 10^0 = 1[/tex]
or, I = 12 lumens
Therefore the light intensity at the surface of the water is 12 lumens.
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Tina is selling tickets for a fundraiser.
She wants to sell more than $300 worth
of tickets. The inequality 12t> 300 can
be used to determine the number of
tickets, t, she must sell in order to meet
her goal. Which number line represents
the solution to this inequality? (6. 9B |
6. 1A, 6. 1B, 6. 10, 6. 1F)
10
20
30
B
to
10
20
30
+
С
+o
+
10
20
30
D
+
10
O
20
30
The number line that represents the solution to this inequality is 6.10, with an open circle at 25 and shading to the right.
To solve the inequality 12t > 300, we need to isolate t on one side of the inequality. We can do this by dividing both sides by 12:
12t/12 > 300/12
t > 25
This means that Tina must sell more than 25 tickets in order to meet her goal of selling more than $300 worth of tickets.
To represent this solution on a number line, we can start by plotting a point at 25. Since the inequality is greater than (>) and not greater than or equal to (≥), we use an open circle at 25.
Then, we need to shade the area to the right of 25 to represent all the possible values of t that satisfy the inequality. This is because any value of t greater than 25 will make 12t greater than 300.
Out of the answer choices given, the number line that represents the solution to this inequality is 6.10, with an open circle at 25 and shading to the right.
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Emma is making a scale drawing of her farm using the scale 1 centimeter to 2. 5 feet. In the drawing, she drew a well with a diameter of 0. 5 ccentimeter. Which is the closest to the actual circumference of the well?
The circumference of the well is 3.93 ft.
Given, Emma is making a scale drawing of her farm using the scale 1 cm=2.5 ft
Diameter of the well she drew = 0.5 cm
We need to convert the diameter of the well from centimeters to feet, using the given scale.
i.e. 0.5cm = 2.5/2 = 1.25 ft
We know the radius is half of the diameter.
So, r = 1.25/2 = 0.625
We know that the formula for the circumference of a circle is C = 2πr
C = 2*3.14*0.625
= 3.93 ft
Hence, the circumference of the well is 3.93 ft.
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Find 30% of 70. HELPPP
Answer:
21
Step-by-step explanation:
70 · .30 = 21
The slant height if the cone is 13 cm. What is the volume of a cone having a radius of 5 cm and a slant height of 13 cm.
The formula for the volume of a cone is:
V = (1/3)πr^2h
where r is the radius of the base of the cone and h is the height of the cone.
We are given that the radius of the cone is 5 cm and the slant height is 13 cm. We can use the Pythagorean theorem to find the height of the cone:
h^2 = l^2 - r^2
where l is the slant height of the cone. Substituting the given values, we get:
h^2 = 13^2 - 5^2
h^2 = 144
h = 12
Now we can substitute the values of r and h into the formula for the volume of the cone:
V = (1/3)πr^2h
V = (1/3)π(5^2)(12)
V = (1/3)π(25)(12)
V = (1/3)π(300)
V = 100π
Therefore, the volume of the cone is 100π cubic centimeters.
list all the Factors. circle the GCF.
6:
9:
list 7 multiples.Circle the LCM.
5:
2:
Answer:
List all the factors
6: 3, 2, 1 (6)
9:3,(9),1
5:(5),1
2:(2),1
Step-by-step explanation:
An oil tank is the shape of a right rectangular prism. The inside of the tank is 36. 5 cm long, 52 cm wide, and 29 cm
high. If 45 liters of oil have been removed from the tank since it was full, what is the current depth of oil left in the
tank?
The current depth of oil left in the tank is approximately 4.64 cm.
The volume of the oil tank can be found by multiplying its length, width, and height:
Volume of the oil tank = length x width x height
= 36.5 cm x 52 cm x 29 cm
= 53,854 cubic cm
If 45 liters of oil have been removed from the tank, the current volume of oil in the tank is:
Current volume of oil = Total volume of tank - Volume of oil removed
= 53,854 cubic cm - 45,000 cubic cm (1 liter = 1000 cubic cm)
= 8,854 cubic cm
Let's assume that the depth of oil left in the tank is x cm. Then the volume of oil left in the tank can be found by multiplying the length, width, and depth of oil:
Volume of oil left in tank = length x width x depth of oil
= 36.5 cm x 52 cm x x cm
= 1906x cubic cm
Now we can set up an equation to find the value of x:
1906x = 8,854
Dividing both sides by 1906, we get:
x = 4.64 cm
Therefore, the current depth of oil left in the tank is approximately 4.64 cm.
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In QRS, the measure of angle S=90°, the measure of angle Q=6°, and RS = 20 feet. Find the
length of SQ to the nearest tenth of a foot.
R
20
6°
s
Q
X
The length of SQ to the nearest tenth of a foot is approximately 2.1 feet.
To find the length of SQ, we can use trigonometry. First, we can find the measure of angle R by subtracting the measures of angles Q and S from 180°:
R = 180° - 90° - 6° = 84°
Then, we can use the sine function to find the length of SX (which is equal to SQ):
sin(Q) = SQ / RS
sin(6°) = SQ / 20
SQ = 20 * sin(6°)
SQ ≈ 2.07 feet (rounded to the nearest tenth of a foot)
Therefore, the length of SQ to the nearest tenth of a foot is approximately 2.1 feet.
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Your team arrived to the scene at 9:30 am and found the temperature of the body at 85 degrees. The team
continued to help collect evidence and noted that the thermostat was set at 72 degrees. After collecting
evidence for one hour, your team checked the body temperature again and found it to now be at 83. 3
degrees
Your team must figure out what time the murder took place.
The murder took place approximately 1.17 hours before the team arrived, which is 8:13 am.
Assuming that the body follows Newton's law of cooling, we can use the formula:
T(t) = Tm + (Ta - Tm) * e^(-kt),
where T(t) is the body temperature at time t, Tm is the temperature of the surrounding medium (in this case, the room), Ta is the initial temperature of the body, and k is a constant that depends on the properties of the body and the surrounding medium.
We can use the information given to find k:
At t = 0 (when the murder took place), T(0) = Ta = unknown
At t = 0.5 hours (30 minutes after the murder), T(0.5) = 85 degrees
At t = 1.5 hours (90 minutes after the murder), T(1.5) = 83.3 degrees
Using the formula above, we can write two equations:
85 = Ta + (72 - Ta) * e^(-0.5k)
83.3 = Ta + (72 - Ta) * e^(-1.5k)
Solving for Ta in the first equation, we get:
Ta = 72 + (85 - 72) / e^(-0.5k) = 72 + 13 / e^(-0.5k)
Substituting this expression for Ta into the second equation, we get:
83.3 = (72 + 13 / e^(-0.5k)) + (72 - (72 + 13 / e^(-0.5k))) * e^(-1.5k)
Simplifying and solving for e^(-0.5k), we get:
e^(-0.5k) = 0.979
the natural logarithm of both sides, we get:
-0.5k = ln(0.979)
Solving for k, we get:
k = -2 * ln(0.979) / 1 = 0.0427
Now we can use the formula again to find Ta:
Ta = 72 + (85 - 72) / e^(-0.5k) = 72 + 13 / e^(-0.5*0.0427) = 78.1 degrees
So the initial temperature of the body was 78.1 degrees.
To find the time of death, we can use the formula again and solve for t when T(t) = 78.1:
78.1 = 72 + (Ta - 72) * e^(-0.0427t)
Substituting Ta = 85 (the initial temperature of the body) and solving for t, we get:
t = -ln((85 - 72) / (78.1 - 72)) / 0.0427 = 1.17 hours
Therefore, the murder took place approximately 1.17 hours before the team arrived, which is 8:13 am.
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Clayton leased an SUV for his business. The lease cost $421.38 per month for 48 months. He paid a $2,500 deposit, an $85 title fee, and a $235 license fee. Find the total lease cost.
The total lease cost for Clayton's SUV is $23,056.24.
To solve this problemBefore any additional fees or deposits, the total lease cost is $421.38 per month for 48 months, which equals:
Total cost of the lease = $421.38/month x 48 months = $20,236.24
Clayton also paid a $2,500 down payment, a $85 title charge, and a $235 license cost in addition to the monthly lease payments.
The entire cost of the lease is $20,236.24 + $2,500 + $85 + $235 = $23,056.24 in total.
Therefore, the total lease cost for Clayton's SUV is $23,056.24.
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A publisher reports that 30% of their readers own a laptop. a marketing executive wants to test the claim that the percentage is actually different from the reported percentage. a random sample of 130 found that 20% of the readers owned a laptop. find the value of the test statistic. round your answer to two decimal places.
The value of the test statistic is approximately -2.49
To find the value of the test statistic for the marketing executive's claim that the percentage of laptop owners is different from the reported 30%, we will use the following formula for a proportion hypothesis test:
[tex]Test Statistic (Z) =\frac{ (Sample Proportion - Hypothesized Proportion)}{Standard Error}[/tex]
Here are the given values:
- Hypothesized proportion (p) = 0.30
- Sample size (n) = 130
- Sample proportion (p-hat) = 0.20
First, we need to calculate the standard error (SE) using this formula:
[tex]SE+\frac{\sqrt{p(1-p)} }{n}[/tex]
[tex]SE+\frac{\sqrt{0.30(1-0.30)} }{130}[/tex]
[tex]SE=\sqrt{\frac{0.21}{130} }[/tex]
[tex]SE=\sqrt{0.0016153846}[/tex]
[tex]SE = 0.04019[/tex]
Now, we can calculate the test statistic (Z) using the given formula:
[tex]Z=\frac{ (0.20 - 0.30)}{0.04019}[/tex]
[tex]Z=\frac{-0.10}{ 0.04019}[/tex]
[tex]Z = -2.49[/tex]
So, the value of the test statistic is approximately -2.49, rounded to two decimal places.
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There are 30 chocolates in a box, all identically shaped. There are 5 filled with coconut and 10 filled with caramel. The other 15 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. What is the probability of selecting a caramel chocolate both times? Are the events of selecting a caramel chocolate on your first pick and selecting a caramel chocolate on your second pick indipendent or dependent? Round to three decimal places
The probability of selecting a caramel chocolate both times is approximately 0.103.
The events of selecting a caramel chocolate on each pick are dependent since the probability of the second pick depends on the outcome of the first pick.
First, we need to calculate the probability of selecting a caramel chocolate on the first pick, which is 10/30 or 1/3. After eating the first chocolate, there will be 29 chocolates left in the box, and 9 of them will be caramel-filled. So, the probability of selecting a caramel chocolate on the second pick, given that the first pick was a caramel chocolate and it was eaten, is 9/29.
To find the probability of selecting a caramel chocolate both times, we need to multiply the probabilities of the two events together, since they are independent:
P(caramel and caramel) = P(caramel on first pick) * P(caramel on second pick | first pick was caramel)
= (1/3) * (9/29)
= 0.103 or 0.1034 rounded to four decimal places.
Therefore, the probability of selecting a caramel chocolate both times is approximately 0.103.
The events of selecting a caramel chocolate on the first pick and selecting a caramel chocolate on the second pick are dependent events since the probability of selecting a caramel chocolate on the second pick changes based on what was selected on the first pick.
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Find all solutions of the equation in the interval [0, 2π). Show formula and steps used, not a calculator problem. (8 csc x - 16)(4 cos x - 4) = 0
The solutions for the equation in the interval [0, 2π) are x = 0, x = π/6, and x = 5π/6.
To find all solutions of the equation (8 csc x - 16)(4 cos x - 4) = 0 in the interval [0, 2π), we can set each factor equal to zero and solve for x separately.
1) 8 csc x - 16 = 0
8 csc x = 16
csc x = 2
Recall that csc x = 1/sin x, so:
1/sin x = 2
sin x = 1/2
In the interval [0, 2π), sin x = 1/2 at x = π/6 and x = 5π/6. So, the solutions for this part are x = π/6 and x = 5π/6.
2) 4 cos x - 4 = 0
4 cos x = 4
cos x = 1
In the interval [0, 2π), cos x = 1 at x = 0 and x = 2π. However, since 2π is not included in the interval, we only have x = 0 as a solution for this part.
Combining both parts, the solutions for the equation in the interval [0, 2π) are x = 0, x = π/6, and x = 5π/6.
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(1 point) Consider a piece of wire with uniform density. It is the quarter of a circle in the first quadrant. The circle is centered at the origin and has radius 5. Find the centroid (cy) of the wire. =y= (1 point) Compute the total mass of a wire bent in a quarter circle with parametric equations: 2 = 9 cost, y=9 sint, 0
The total mass of the wire is [tex]M = 9\rho * (\pi/2).[/tex]
How to find the total mass of the wire?Using the formula for finding the centroid of a two-dimensional object with uniform density:
cy = (1/Area) * ∫(y*dA)
The equation of the circle is [tex]x^2 + y^2 = 25[/tex]. Solving for y, we get:
[tex]y = \sqrt(25 - x^2)[/tex]
Since the wire is in the first quadrant, the limits of integration are 0 ≤ x ≤ 5 and 0 ≤ y ≤ [tex]\sqrt(25 - x^2).[/tex]
To find the area of the wire, we integrate:
[tex]Area = \int \int dA = \int 0^5 \int 0^{\sqrt(25-x^2)}dy dx[/tex]
[tex]= \int 0^{5 (sqrt(25-x^2))}dx[/tex]
[tex]= (1/2) * [25sin^{(-1)(x/5)} + x\sqrt(25-x^2)] from 0 to 5[/tex]
[tex]= (1/2) * [25\pi/2] = 25\pi/4[/tex]
To find the centroid (cy), we integrate:
[tex]cy = (1/Area) * \int(ydA) = (1/(25\pi/4)) * \int0^5 \int0^{\sqrt(25-x^2)} y dy dx[/tex]
[tex]= (4/25*\pi) * \int0^5 [(1/2)*y^2]_0^{\sqrt(25-x^2)} dx[/tex]
[tex]= (4/25\pi) * \int 0^5 [(1/2)(25-x^2)] dx[/tex]
[tex]= (4/25\pi) * [(25x - (1/3)*x^3)/2]_0^5[/tex]
[tex]= (4/25\pi) * [(255 - (1/3)*5^3)/2][/tex]
[tex]= 50/3[/tex]
Therefore, the centroid of the wire is cy = 50/3.
Now use the formula for the mass of a thin wire for total mass:
M = ∫ρ ds
Since the wire has uniform density, the linear density is constant and can be factored out of the integral:
M = ρ * ∫ds
The differential element of arc length is:
[tex]ds = \sqrt(dx^2 + dy^2) = \sqrt((-9sin t)^2 + (9cos t)^2) dt[/tex]
[tex]= 9\sqrt(sin^2 t + cos^2 t) dt = 9 dt[/tex]
Integrating from 0 to pi/2, we get:
[tex]M = \rho * \int ds = \rho * \int 0^{(\pi/2)} 9 dt[/tex]
[tex]= 9\rho * [t]_0^{(\pi/2)} = 9\rho * (\pi/2)[/tex]
Therefore, the total mass of the wire is [tex]M = 9\rho * (\pi/2).[/tex]
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what the size of angle g 82,104,76
Answer:
angle g is 98 degrees.
Step-by-step explanation:
assuming the figure is a quadrilateral,
angle g + 82 + 104 + 76 = 360 ( Property of Quadrilateral)
262 + angle g = 360
angle g = 98 degrees
A favorite activity at LNHS is throwing paper
balls into the trashcan while the teacher isn't
looking. Suppose a paper ball is shot from 5 feet
off the ground, and the paper ball reaches a
height of 10 feet after 3 seconds.
*Write the equation that models the height (h)
of the paper ball at any given second (t).
Help me!!
The equation that models the height (h) of the paper ball at any given second (t) is: [tex]h = -16t^2 + 49.67t + 5.[/tex]
To write the equation that models the height (h) of the paper ball at any given second (t), we can use the formula:
[tex]h = -16t^2 + vt + s[/tex]
where v is the initial velocity (in feet per second), s is the initial height (in feet), and t is the time (in seconds).
In this case, we know that the paper ball was shot from 5 feet off the ground, so s = 5. We also know that the paper ball reached a height of 10 feet after 3 seconds, so we can use this information to find the initial velocity:
[tex]h = -16t^2 + vt + s[/tex]
[tex]10 = -16(3)^2 + v(3) + 5[/tex]
10 = -144 + 3v + 5
149 = 3v
v = 49.67 (rounded to two decimal places)
Now we can substitute the values for v and s into the equation:
[tex]h = -16t^2 + vt + s\\h = -16t^2 + 49.67t + 5[/tex]
Therefore, the equation that models the height (h) of the paper ball at any given second (t) is:
[tex]h = -16t^2 + 49.67t + 5.[/tex]
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In ΔUVW, the measure of ∠W=90°, UV = 4. 7 feet, and WU = 2. 2 feet. Find the measure of ∠U to the nearest degree
The measure of angle U in triangle UVW is approximately 28 degrees. This is found by using the inverse tangent function to solve for angle U given the lengths of two sides and the fact that angle W is a right angle.
To find the measure of ∠U in ΔUVW, we can use trigonometry. We know that sin(∠U) = opposite/hypotenuse, which is equal to UW/VW. Therefore, we can plug in the given values and solve for sin(∠U)
sin(∠U) = UW/VW = 2.2/4.7 = 0.4681
Next, we can use the inverse sine function (sin⁻¹) to find the measure of ∠U
∠U = sin⁻¹(0.4681) = 28.34 degrees (rounded to the nearest degree)
Therefore, the measure of ∠U in ΔUVW is approximately 28 degrees.
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Type the correct answer in the box.
The given equation, V = 1/3 πr²h, solved for h is:
h = 3V / πr²
Subject of formulae: Solving the equation for hFrom the question, we are to solve the give equation for h
From the given information,
The given equation is
V = 1/3 πr²h
To solve the equation for h, we will isolate h
Solving the equation for h
V = 1/3 πr²h
Multiply both sides of the equation by 3
3 × V = 3 × 1/3 πr²h
3V = πr²h
Divide both sides of the equation by πr²
3V / πr² = πr²h / πr²
3V / πr² = h
This can be written as
h = 3V / πr²
Hence, the equation solved for h is:
h = 3V / πr²
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Quadratic function for (1,-3) in vertex form
The quadratic function in vertex form that passes through the point (1, -3) is: f(x) = (x - 1)² - 3
What is vertex form?
Vertex form is a way of expressing a quadratic function of the form:
f(x) = a(x - h)² + k
where (h, k) is the vertex of the parabola, and a is a constant that determines the shape and direction of the parabola.
The quadratic function in vertex form is given by:
f(x) = a(x - h)² + k
where (h, k) is the vertex of the parabola.
We are given the point (1, -3), which lies on the parabola. This means that:
f(1) = -3
Substituting x = 1 into the vertex form of the equation, we get:
f(1) = a(1 - h)² + k
-3 = a(1 - h)² + k
Since we don't know the value of h or a, we can't solve for k directly. However, we can use the vertex form of the equation to find the values of h and k.
The vertex of the parabola is the point (h, k). Since the parabola passes through the point (1, -3), we know that the vertex lies on the axis of symmetry, which is the vertical line x = 1.
Therefore, the x-coordinate of the vertex is h = 1. Substituting this into the equation above, we get:
-3 = a(1 - 1)² + k
-3 = a(0) + k
k = -3
Now that we know the value of k, we can substitute it back into the equation above and solve for a:
-3 = a(1 - h)² + k
-3 = a(1 - 1)² + (-3)
-3 = a(0) - 3
a = 1
Therefore, the quadratic function in vertex form that passes through the point (1, -3) is:
f(x) = (x - 1)² - 3
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Which statement is true about the streets? Select all that apply. A. First Street intersects with Second Street and Third Street. B. Second Street is perpendicular to Third Street. C. First Street and Third Street are parallel. D. Second Street and Third Street are parallel. E. First Street is perpendicular to Second Street and Third Street. 6 /
The correct options are: A and D
Streets 2 and 3 are parallel and Street 1 is intersecting it
What is a Parallel Line and Intersections?Parallel lines are two or more straight lines that continue indefinitely without ever crossing each other, despite their extended lengths. They have an equal inclination and remain the same distance apart at all times. Consequently, intersections will never occur between them.
On the contrary, if non-parallel lines exist, they intersect to create one point, famously known as the 'point of intersection'. This specific point supplies the solution to the system of equations formed by the two lines.
Hence, we can see from the given image that Streets 2 and 3 are parallel and Street 1 is intersecting it
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The ratio of m angle wxz to m angle zxy is 11:25. what is m angle zxy
The measure of angle zxy is 125 degrees.
To solve the problem, we can use the fact that the sum of the measures of two adjacent angles is 180 degrees. Let's call the measure of angle zxy "x".
We know that the ratio of m angle wxz to m angle zxy is 11:25, which means that:
m angle wxz : m angle zxy = 11 : 25
We can write this as an equation:
m angle wxz / m angle zxy = 11/25
We also know that the two angles are adjacent, so their measures add up to 180 degrees:
m angle wxz + m angle zxy = 180
Now we can use these two equations to solve for x:
m angle wxz / x = 11/25
m angle wxz = (11/25)x
Substituting this into the second equation:
(11/25)x + x = 180
(36/25)x = 180
x = (25/36) * 180
x = 125
Therefore, the measure of angle zxy is 125 degrees.
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HA Leonardo le compraron 3 libros por su cumpleaños. Si por dos se pagaron 760 y la cuenta fue de 1125 cuanto costó el tercer libro
Sure, I'd be happy to help you with that. Based on the information provided, we know that HA Leonardo received three books for his birthday and two of them cost a total of 760. To find out the cost of the third book, we need to subtract the cost of the two books from the total amount paid, which is 1125.
To do this, we can use a simple equation:
Total cost of three books - Total cost of two books = Cost of third book
So, we can plug in the values we know:
1125 - 760 = Cost of third book
Solving for the cost of the third book:
365 = Cost of third book
Therefore, the third book cost 365.
In summary, HA Leonardo received three books for his birthday and two of them cost 760. The total amount paid was 1125, so the cost of the third book was 365.
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7 2 14 3 8 11 5 each time a card is picked it is replaced estimate the expected number of even numbers picked in 35 picks
We can estimate that the expected number of even numbers picked in 35 picks is 15.
To estimate the expected number of even numbers picked in 35 picks, we need to first understand the probability of picking an even number in one pick. Out of the seven given numbers, there are three even numbers (2, 14, 8) and four odd numbers (7, 3, 11, 5). Therefore, the probability of picking an even number in one pick is 3/7.
To find the expected number of even numbers picked in 35 picks, we can multiply the probability of picking an even number in one pick (3/7) by the number of picks (35).
Expected number of even numbers picked = (3/7) x 35 = 15
Therefore, we can estimate that the expected number of even numbers picked in 35 picks is 15. This means that if we were to repeat the process of picking a card and replacing it 35 times, we would expect to pick 15 even numbers on average.
It is important to note that this is an estimate and the actual number of even numbers picked may vary. However, this estimation gives us a good idea of what to expect on average.
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Please hurry I need it ASAP
Answer: d=2√13
Step-by-step explanation:
You need to use the distance formula or pythagorean. Pythagorean is simpler. Let's use that.
c²=a²+b²
c= distance
a = how far point went in x direction =4
b=how far went in y direction =6
plug in:
d²=4²+6²
d²=16+36
d²=52 take square root of both sides
d=√52
d=√(4*13 4 and 13 are factors of 52
d=2√13 take square root of 4
A parallelogram has an area of
25. 2
c
m
2
25. 2 cm
2
and a height of
4
c
m
4 cm. Use paper to write an equation that relates the height, base, and area of the parallelogram. Solve the equation to find the length of the base then what is the length of the base? (Can someone help me out please)
If the parallelogram has an area of 25.2 cm² and the height is 4 cm, the length of the base is 6.3 cm.
To start, we know that the area of a parallelogram is given by the formula:
A = bh
where A is the area, b is the length of the base, and h is the height. We also know that the area of the parallelogram in this case is 25.2 cm² and the height is 4 cm.
Substituting these values into the formula, we get:
25.2 = b(4)
To solve for b, we can divide both sides by 4:
b = 25.2/4
b = 6.3
So the length of the base is 6.3 cm.
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Mary creates a stack of 10 of piece am and a stack of 8 of piece N. Both stacks have equal volumes. Create an equation relating h and k
Let's assume that the pieces am and N have heights of h_am and h_N respectively, and let k be the number of times the height of piece N fits into the height of piece am (i.e., k is the ratio of the height of piece am to the height of piece N).
We know that the volume of each stack is equal. Let's use the following variables:
- h for the height of each piece of A
- k for the height of each piece of N
- 10 for the number of pieces in stack A
- 8 for the number of pieces in stack N
The equation for the volume of each stack is:
Volume of stack A = h x 10
Volume of stack N = k x 8
Since we know the volumes are equal, we can set the two equations equal to each other:
h x 10 = k x 8
To create an equation relating h and k, we can solve for one variable in terms of the other:
h = (8/10)k
or
k = (10/8)h
Either equation shows how h and k are related to each other. For example, if we know the value of h, we can use the first equation to find k.
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tomas earns 0.5% commision on the sale price of a new car. On wednesday, he sells a new car for $24,500. How much commison does tomas earn on this sale
Tomas earns a commission of $122.50 on the sale of the new car.
Tomas earns a 0.5% commission on the sale price of a new car. On Wednesday, he sells a new car for $24,500. To determine the commission Tomas earns, we need to multiply the sale price by the commission rate. The commission rate is given as 0.5%, which can be expressed as a decimal by dividing by 100. So, 0.5% is equal to 0.005 as a decimal.
Now, we can calculate Tomas's commission by multiplying the sale price by the commission rate. In this case, we multiply $24,500 by 0.005:
$24,500 x 0.005 = $122.50
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If the area of the top of a cylinder is 16 square cm and the height is 8 cm, what is the volume of the cylinder?
Answers:
A. 128 cm cubed
B. 512 cm cubed
C. 256 cm cubed
D. 64 cm cubed
A. 128CM CUBED
Step-by-step explanation:
THE FORMULLA : it's v(volume) =AB (BAZE AREA OR TOP AREA ) × HEIGHT SO
16 SQUARE CM ×8CM
=128CM CUBEDA baker has small and large bags of sugar for making cakes. The large bag contains 30 cups of sugar and it's 2. 5 times larger than the small bag. The small bag contains enough sugar to make nine cakes and have. 75 cups of sugar remaining
How many cakes can be made with a large bag of sugar?
The number of cakes that can be made with a large bag of sugar, we first need to determine the amount of sugar in a small bag and then calculate the amount of sugar needed for one cake.
1. Find the amount of sugar in a small bag:
Since the large bag contains 30 cups of sugar and is 2.5 times larger than the small bag, we can write the equation:
Small bag = Large bag / 2.5
Small bag = 30 cups / 2.5
Small bag = 12 cups of sugar
2. Determine the amount of sugar needed for one cake:
The small bag contains enough sugar to make 9 cakes and have 0.75 cups of sugar remaining. So, we can subtract the remaining sugar from the total amount in the small bag:
Sugar used for 9 cakes = 12 cups - 0.75 cups
Sugar used for 9 cakes = 11.25 cups
Now, we can find the amount of sugar needed for one cake:
Sugar per cake = Sugar used for 9 cakes / 9
Sugar per cake = 11.25 cups / 9
Sugar per cake = 1.25 cups
3. Calculate the number of cakes that can be made with a large bag of sugar:
Cakes from large bag = Large bag sugar / Sugar per cake
Cakes from large bag = 30 cups / 1.25 cups
Cakes from large bag = 24
Therefore, a baker can make 24 cakes with a large bag of sugar.
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A scientist recorded the movement of a pendulum for 12 s. The scientist began recording when the pendulum was at its resting position. The pendulum then moved right (positive displacement) and left (negative displacement) several times. The pendulum took 6 s to swing to the right and the left and then return to its resting position. The pendulum’s furthest distance to either side was 7 in. Graph the function that represents the pendulum’s displacement as a function of time. (a) Write an equation to represent the displacement of the pendulum as a function of time. (B) Graph the function. (Please help me answer this for my friend. I am so baffled)
The equation for the displacement of the pendulum as a function of time is: displacement = 7 sin(π/3 t)
How to explain the equationThe motion of a pendulum can be modeled using a sine function:
displacement = A sin(ωt + φ)
where A is the amplitude (the furthest distance from the equilibrium point), ω is the angular frequency (related to the period T by ω = 2π/T), t is time, and φ is the phase angle (determines the starting point of the oscillation).
In this case, the pendulum has an amplitude of 7 inches and a period of 6 seconds (since it takes 6 seconds to swing to one side and then back to the other). Therefore, the angular frequency is:
ω = 2π/T = 2π/6 = π/3
The phase angle is 0, since the pendulum starts at its equilibrium position.
So, the equation for the displacement of the pendulum as a function of time is:
displacement = 7 sin(π/3 t)
where t is measured in seconds and the displacement is measured in inches.
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describe the likelihood of the next elk caught being unmarked
The probability of the next elk caught being unmarked is 0.96 when the total number of elks is 5625 and the number of elks marked is 225.
A probability is given by the number of desired outcomes divided by the number of total outcomes.
Total number of elks = 5625
Number of elks marked = 225
We need to find the total number of elks not marked or unmarked we can find it by,
= 5625 - 225
= 5500
Therefore, the total number of elks unmarked is 5500.
We can determine determined the likelihood of the next elk caught being unmarked by using probability. The probability is given by:
P = 5500/5625
= 44 / 45
= 0.96
Therefore, The total number of elks unmarked is 0.96.
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The complete question is,
Describe the likelihood of the next elk caught being unmarked.
